Cost of facilitation: invasive grasses limit recruitment of benefactor shrubs.

ecoblender

alex.filazzola

Abstract

Shrubs facilitate the abundance and productive of annual plants in desert ecosystems.However, these shrub microhabitats favour plant species with competitive life histories. Ephedra californica is a dominant shrub in the San Joaquin desert that has been identified as a facilitator. Here, we explore the factors that limit the Ephedra californica recruitment into the San Joaquin desert including substrate, water availability, and herbivory. We also explore the role of the invasive grass Bromus madritensis on limiting establishment of E. californica. Vegetation surveys were conducted in the field during 2013 and collected seed was then used to conduct two greenhouse trials. The first explore germination and establishment techniques for E. california and the optimal substrate. The second examined E. californica establishment in present of the invasive B. madritensis responding to different water levels and herbivory. These results can have implications for land managers in the San Joaquin Valley to maintain native shrub biodiversity in the region.

---

## load libraries
library(tidyverse)
# library(OIsurv)
library(lsmeans)
library(ggthemes)
library(ape)

## load data
substrate <-read.csv("data/Ephedra.substrate.csv")
recruit <-read.csv("data/Ephedra.recruitment.csv")
landscape <-read.csv("data/ephedra.landscape.csv")

##load functions
## inverse hyperbolic sine transformation 
ihs <- function(x) {
    y <- log(x + sqrt(x ^ 2 + 1))
    return(y)
}
se <- function(x, ...) sqrt(var(na.omit(x))/length(na.omit(x)))
source("functions.r")

Ephedra characteristics at the landscape

avg.size <- landscape %>% summarize(h=mean(H), d1=mean(D1), area=mean(Area), density=mean(Shrub.density), rdm=mean(RDM.2013),h.se=se(H), d1.se=se(D1), area.se=se(Area), density.se=se(Shrub.density), rdm.se=se(RDM.2013))
avg.size

##          h       d1     area     density      rdm       h.se      d1.se
## 1 1.332925 3.446412 9.321902 0.004318859 7.042223 0.01506635 0.05137079
##     area.se   density.se    rdm.se
## 1 0.2708882 6.272347e-05 0.2109119

Ephedra recruitment at landscape

## compare ephedra size and density across landscape
landscape[,"area.group"] <- as.numeric(cut(landscape$Log.area,20))
hist(landscape$area.group)

mean.area <- landscape %>% group_by(area.group) %>%  summarize(rdm=mean(RDM.2013), area=mean(Log.area), density=mean(Shrub.density))

ggplot(mean.area) + geom_point(aes(x=density, y=area), size=3)+ylab("log (area of shrub)")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16)) + xlab(expression("shrub density (m"^"2"*")")) +  stat_smooth(method="lm", formula= y~x,aes(x=density, y=area))

m1 <- lm(area~density, data=mean.area)
summary(m1)

## 
## Call:
## lm(formula = area ~ density, data = mean.area)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.82510 -0.26068  0.01197  0.22216  1.16732 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     9.3959     0.9852   9.537 1.84e-08 ***
## density     -1706.0323   223.6888  -7.627 4.81e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5569 on 18 degrees of freedom
## Multiple R-squared:  0.7637, Adjusted R-squared:  0.7506 
## F-statistic: 58.17 on 1 and 18 DF,  p-value: 4.806e-07

## convert RDM to kg

ggplot(mean.area) + geom_point(aes(x=rdm*20, y=density), size=mean.area$area+1)+xlab("residual dry matter (kg / acre)")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16)) + ylab(expression("shrub density (m"^"2"*")")) +  stat_smooth(method="lm", formula= y~x,aes(x=rdm*20, y=density))

m2 <- lm(log(rdm)~density, data=mean.area)
summary(m2)

## 
## Call:
## lm(formula = log(rdm) ~ density, data = mean.area)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.32696 -0.09127 -0.02044  0.05849  0.46804 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.1851     0.3294   9.670 1.49e-08 ***
## density     -279.3744    74.7892  -3.735  0.00151 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1862 on 18 degrees of freedom
## Multiple R-squared:  0.4367, Adjusted R-squared:  0.4054 
## F-statistic: 13.95 on 1 and 18 DF,  p-value: 0.001514

m1 <- lm(Shrub.density ~ RDM.2013, data=landscape) ## compare RDM with shrub density 

m3 <- manova(cbind(Shrub.density, Log.area) ~ RDM.2013, data=landscape)
summary(m3)

##            Df   Pillai approx F num Df den Df   Pr(>F)    
## RDM.2013    1 0.028461   10.121      2    691 4.65e-05 ***
## Residuals 692                                             
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary.aov(m3)

##  Response Shrub.density :
##              Df     Sum Sq    Mean Sq F value Pr(>F)
## RDM.2013      1 0.00000172 1.7228e-06  0.6307 0.4274
## Residuals   692 0.00189042 2.7318e-06               
## 
##  Response Log.area :
##              Df Sum Sq Mean Sq F value    Pr(>F)    
## RDM.2013      1   9.50  9.5046  17.183 3.815e-05 ***
## Residuals   692 382.77  0.5531                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Ephedra optimal substrate

substrate[,"Sand"] <- as.factor(substrate$Sand)
substrate[,"census"] <- as.factor(substrate$census)

m1 <- aov(height ~ Micro * Sand,  data=subset(substrate, census==10))
summary(m2) ## nothing significant


## compare shade on survival of ephedra
my.surv <- Surv(as.numeric(substrate$census), substrate$survival)
fit1 <- survfit(my.surv~Micro, data=substrate)
summary(fit1)


par(mar=c(4.5,4.5,.5,.5))
plot(fit1, col="white", ylim=c(0.2,1), xlim=c(0.9,10.1), ylab="Estimated Survival Function", xlab="Census", cex.lab=1.5, cex.axis=1.3)
lines(1:10,summary(fit1)[[10]][1:10], col="#E69F00", lty=2) ## upper
lines(1:10,summary(fit1)[[6]][1:10], col="#E69F00", lwd=2) ## value sun
lines(1:10,summary(fit1)[[11]][1:10], col="#E69F00", lty=2) ## lower
lines(1:10,summary(fit1)[[10]][11:20], col="#56B4E9", lty=2) ## upper
lines(1:10,summary(fit1)[[6]][11:20], col="#56B4E9", lwd=2) ## value shade
lines(1:10,summary(fit1)[[11]][11:20], col="#56B4E9", lty=2) ## lower
legend(1.8, 0.35, c("Sun","Shade"), lty=1, lwd=3, col=c("#E69F00","#56B4E9"), cex=1.5)

coxph.fit <- coxph(my.surv ~ Micro, method="breslow", data=substrate)
coxph.fit 


## compare sand on survival of ephedra
my.surv <- Surv(as.numeric(substrate$census), substrate$survival)
fit2 <- survfit(my.surv~Sand, data=substrate)
summary(fit2)


test <- substrate %>% group_by(census,Sand) %>%  summarize(count=sum(survival),avg=mean(survival))
test <- data.frame(test)

par(mar=c(4.5,4.5,.5,.5))
plot(fit2, col="white", ylim=c(0.2,1), xlim=c(0.9,10.1), ylab="Estimated Survival Function", xlab="Census", cex.lab=1.5, cex.axis=1.3)
lines(1:10,summary(fit2)[[10]][1:10], col="#E69F00", lty=2) ## upper
lines(1:10,summary(fit2)[[6]][1:10], col="#E69F00", lwd=2) ## value sand 0
lines(1:10,summary(fit2)[[11]][1:10], col="#E69F00", lty=2) ## lower
lines(1:10,summary(fit2)[[10]][11:20], col="#56B4E9", lty=2) ## upper
lines(1:10,summary(fit2)[[6]][11:20], col="#56B4E9", lwd=2) ## value sand 25
lines(1:10,summary(fit2)[[11]][11:20], col="#56B4E9", lty=2) ## lower
lines(1:10,summary(fit2)[[10]][21:30], col="#009E73", lty=2) ## upper
lines(1:10,summary(fit2)[[6]][21:30], col="#009E73", lwd=2) ## value sand 50
lines(1:10,summary(fit2)[[11]][21:30], col="#009E73", lty=2) ## lower
lines(1:10,summary(fit2)[[10]][31:40], col="#CC79A7", lty=2) ## upper
lines(1:10,summary(fit2)[[6]][31:40], col="#CC79A7", lwd=2) ## value sand 75
lines(1:10,summary(fit2)[[11]][31:40], col="#CC79A7", lty=2) ## lower
lines(1:10,summary(fit2)[[10]][41:50], col="#D55E00", lty=2) ## upper
lines(1:10,summary(fit2)[[6]][41:50], col="#D55E00", lwd=2) ## value sand 100
lines(1:10,summary(fit2)[[11]][41:50], col="#D55E00", lty=2) ## lower
legend(1.7, 0.44, c("0%","25%","50%","75%","100%"), lty=1, lwd=3, col=c("#E69F00","#56B4E9","#009E73","#CC79A7","#D55E00"), cex=1.2, title="Sand")

coxph.fit <- coxph(my.surv ~ Sand, method="breslow", data=substrate)
coxph.fit 

## raw number of germinants end trials

end <- subset(substrate, census==10)

## compare microsite

end.means <- end %>% group_by(Micro) %>% summarize(eph=mean(survival), eph.se=se(survival), Height=mean(height, na.rm=T), Height.se=se(height)) %>% gather(measure, value, 2:5) %>% separate(measure, c("Eph",".se")) ## calculate metrics and put long format
end.means[is.na(end.means$.se),3] <- "mean"
end.means <- end.means %>% spread(.se, value)
end.means <- data.frame(end.means)

end.means[,"lower"] <- end.means[,"mean"]-end.means[,"se"]
end.means[,"upper"] <- end.means[,"mean"]+end.means[,"se"]

survival <- subset(end.means, Eph=="eph")

plot1 <- ggplot(survival, aes(x=Micro, y=mean)) + geom_bar(stat="identity") +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=.2)+ylab("average surviving Ephedra plant")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16)) + xlab("Microsite") 

height <- subset(end.means, Eph=="Height")

plot2 <- ggplot(height, aes(x=Micro, y=mean)) + geom_bar(stat="identity") +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=.2)+ylab("average height of Ephedra plant")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16)) + xlab("Microsite") 

require(gridExtra)

grid.arrange(plot1, plot2, ncol=2)
m1 <- glm(survival~ Sand* Micro, data=end, family="binomial")
anova(m1, test="Chisq")

lsmeans(m1, pairwise~Sand)


## survival
end.means <- end %>% group_by(Sand) %>% summarize(eph=mean(survival), eph.se=se(survival))
end.means <- data.frame(end.means)

end.means[,"lower"] <- end.means[,"eph"]-end.means[,"eph.se"]
end.means[,"upper"] <- end.means[,"eph"]+end.means[,"eph.se"]

ggplot(end.means, aes(x=Sand, y=eph)) + geom_bar(stat="identity", fill="#56B4E9") +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=.2)+ylab("average surviving Ephedra plant")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16)) + xlab("Percentage of sand in soil") 


## height

end.means <- end %>% group_by(Sand) %>% summarize(eph=mean(height, na.rm=T), eph.se=se(height, na.rm=T))
end.means <- data.frame(end.means)

end.means[,"lower"] <- end.means[,"eph"]-end.means[,"eph.se"]
end.means[,"upper"] <- end.means[,"eph"]+end.means[,"eph.se"]

ggplot(end.means, aes(x=Sand, y=eph)) + geom_bar(stat="identity", fill="#56B4E9") +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=.2)+ylab("average surviving Ephedra plant")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16)) + xlab("Percentage of sand in soil") 


## most germinants
maximum.germ <- substrate %>% group_by(Micro, Sand, Rep) %>% summarize(eph.max=max(survival))

max.eph <- maximum.germ %>% group_by(Sand) %>% summarize(eph=mean(eph.max,na.rm=T),eph.se=se(eph.max, na.rm=T)) 
max.eph <- data.frame(max.eph)

max.eph[,"lower"] <- max.eph[,"eph"]-max.eph[,"eph.se"]
max.eph[,"upper"] <- max.eph[,"eph"]+max.eph[,"eph.se"]


ggplot(max.eph, aes(x=Sand, y=eph)) + geom_point(fill="black", size=4) +
  geom_errorbar(aes(ymin=lower, ymax=upper), width=.2)+ylab(expression("Average emerged plants of   "*italic("E. californica")))+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16)) + xlab("Percentage of sand in soil") + ylim(0,1) + stat_smooth(method="lm", formula= y~poly(x,2),data=max.eph, aes(x=as.numeric(Sand), y=eph), lwd=1, color="black", lty=2)

m1 <- lm(eph~poly(as.numeric(Sand),2), data=max.eph)
summary(m1)


## Difference between emergence and survival
substrate2 <- subset(substrate, census==10)
substrate2[,"diff"] <- subset(substrate, census==1, "survival")+subset(substrate, census==10,"survival")
substrate2 <- subset(substrate2, diff!=0) ## remove plots that had no plants
substrate2[,"diff"] <- substrate2[,"diff"]-1 ## binomial whether or not survived 


m2 <- glm(diff ~ Micro, family=binomial, data=substrate2)
anova(m2, test="Chisq")

Test of limiting factors - brome

recruit[is.na(recruit)] <- 0

## water
water <- subset(recruit, Treatment == "control" | Treatment=="water")

## germination
water.germ <- water %>% group_by(Density, Lvl) %>% summarize(eph=mean(ephedra.end ),brome=mean(brome.begin))

ggplot(water.germ) + geom_jitter(aes(x=Density, y=brome, fill=Lvl, color=Lvl), size=2)+ylab("number of Bromus germinants")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

m1 <- glm(brome.begin~Density *Lvl, data=water, family=poisson)
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: poisson, link: log
## 
## Response: brome.begin
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)    
## NULL                          299    1275.05             
## Density      1   849.52       298     425.53   <2e-16 ***
## Lvl          2     4.50       296     421.03   0.1053    
## Density:Lvl  2     0.00       294     421.03   0.9985    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## biomass
water.bio <- water %>% group_by(Density, Lvl) %>% summarize(eph=mean(Ephedra.biomass ),brome=mean(brome.biomass))

ggplot(water.bio) + geom_jitter(aes(x=Density, y=brome, fill=Lvl, color=Lvl), size=2)+ylab("final biomass of Brome")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

## clipping
clip <- subset(recruit, Treatment == "control" | Treatment=="clipped")

## germination
clip.germ <- clip %>% group_by(Density, Lvl) %>% summarize(eph=mean(ephedra.end ),brome=mean(brome.begin))

ggplot(clip.germ) + geom_jitter(aes(x=Density, y=brome, fill=Lvl, color=Lvl), size=2)+ylab("number of Bromus germinants")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

## biomass
clip.bio <- clip %>% group_by(Density, Lvl) %>% summarize(eph=mean(Ephedra.biomass ),brome=mean(brome.biomass))

ggplot(clip.bio) + geom_jitter(aes(x=Density, y=brome, fill=Lvl, color=Lvl), size=2)+ylab("final biomass of Brome")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

m1 <- glm(brome.begin~Density *Lvl, data=clip, family=poisson)
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: poisson, link: log
## 
## Response: brome.begin
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)    
## NULL                          299    1332.93             
## Density      1   863.30       298     469.63   <2e-16 ***
## Lvl          2     3.66       296     465.97   0.1605    
## Density:Lvl  2     0.04       294     465.93   0.9814    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## shade
shade <- subset(recruit, Treatment == "control" | Treatment=="shade")

## germination
shade.germ <- shade %>% group_by(Density, Lvl) %>% summarize(eph=mean(ephedra.end ),brome=mean(brome.begin))

ggplot(shade.germ) + geom_jitter(aes(x=Density, y=brome, fill=Lvl, color=Lvl), size=2)+ylab("number of Bromus germinants")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

## biomass
shade.bio <- shade %>% group_by(Density, Lvl) %>% summarize(eph=mean(Ephedra.biomass ),brome=mean(brome.biomass))

ggplot(shade.bio) + geom_jitter(aes(x=Density, y=brome, fill=Lvl, color=Lvl), size=2)+ylab("final biomass of Brome")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

m1 <- glm(brome.begin~Density *Lvl, data=shade, family=poisson)
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: poisson, link: log
## 
## Response: brome.begin
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                          299    1221.52              
## Density      1   804.97       298     416.55 < 2.2e-16 ***
## Lvl          2    13.34       296     403.21  0.001267 ** 
## Density:Lvl  2     0.22       294     402.98  0.894507    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Test of limiting factors - Ephedra

## water
## germination

ggplot(water.germ) + geom_jitter(aes(x=Density, y=eph, fill=Lvl, color=Lvl), size=2)+ylab("number of Ephedra germinants")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

## biomass

ggplot(water.bio) + geom_jitter(aes(x=Density, y=eph, fill=Lvl, color=Lvl), size=2)+ylab("final biomass of Ephedra")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

## clipping

## germination

ggplot(clip.germ) + geom_jitter(aes(x=Density, y=eph, fill=Lvl, color=Lvl), size=2)+ylab("number of Ephedra germinants")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

## biomass

ggplot(clip.bio) + geom_jitter(aes(x=Density, y=eph, fill=Lvl, color=Lvl), size=2)+ylab("final biomass of Ephedra")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

m1 <- glm(ephedra.end~Density *Lvl, data=clip, family=poisson)
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: poisson, link: log
## 
## Response: ephedra.end
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)  
## NULL                          299     220.71           
## Density      1  2.73641       298     217.97  0.09808 .
## Lvl          2  0.34733       296     217.63  0.84058  
## Density:Lvl  2  0.47792       294     217.15  0.78745  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## shade

## germination

ggplot(shade.germ) + geom_jitter(aes(x=Density, y=eph, fill=Lvl, color=Lvl), size=2)+ylab("number of Ephedra germinants")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

##biomass
ggplot(shade.bio) + geom_jitter(aes(x=Density, y=eph, fill=Lvl, color=Lvl), size=2)+ylab("final biomass of Ephedra")+ theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.line = element_line(colour = "black"),panel.background = element_blank(),axis.text=element_text(size=14),axis.title=element_text(size=16))

m1 <- glm(brome.begin~Density *Lvl, data=shade, family=poisson)
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: poisson, link: log
## 
## Response: brome.begin
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                          299    1221.52              
## Density      1   804.97       298     416.55 < 2.2e-16 ***
## Lvl          2    13.34       296     403.21  0.001267 ** 
## Density:Lvl  2     0.22       294     402.98  0.894507    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Summarized GLMs for manuscript

## Water
m1 <- glm(ephedra.end~ Density *Lvl , data=water, family=binomial)
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: ephedra.end
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)  
## NULL                          299     397.45           
## Density      1  2.78375       298     394.66  0.09522 .
## Lvl          2  0.20096       296     394.46  0.90440  
## Density:Lvl  2  0.08676       294     394.37  0.95755  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

m1.bio <- glm(Ephedra.biomass~Density *Lvl, data=subset(water, Ephedra.biomass>0, family=Gamma))
anova(m1.bio, test="Chisq")

## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: Ephedra.biomass
## 
## Terms added sequentially (first to last)
## 
## 
##             Df   Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL                            106   0.057926         
## Density      1 0.00022241       105   0.057704   0.5282
## Lvl          2 0.00019973       103   0.057504   0.8364
## Density:Lvl  2 0.00103890       101   0.056465   0.3949

## Shade
m2 <- glm(ephedra.end~ Density *Lvl, data=shade, family=binomial)
anova(m2, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: ephedra.end
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)   
## NULL                          299     368.20            
## Density      1   0.7330       298     367.46 0.391927   
## Lvl          2  11.4709       296     355.99 0.003229 **
## Density:Lvl  2   1.4327       294     354.56 0.488533   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

m2.bio <- glm(Ephedra.biomass~Density *Lvl , data=subset(shade, Ephedra.biomass>0), family=Gamma)
anova(m2.bio, test="Chisq")

## Analysis of Deviance Table
## 
## Model: Gamma, link: inverse
## 
## Response: Ephedra.biomass
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)  
## NULL                           67     25.637           
## Density      1  0.39889        66     25.238  0.23231  
## Lvl          2  2.02160        64     23.217  0.02691 *
## Density:Lvl  2  0.02846        62     23.188  0.95038  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Clipping
m3 <- glm(ephedra.end~ Density *Lvl, data=clip, family=binomial)
anova(m3, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: ephedra.end
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)  
## NULL                          299     393.19           
## Density      1   4.2054       298     388.98   0.0403 *
## Lvl          2   0.5545       296     388.43   0.7579  
## Density:Lvl  2   0.8190       294     387.61   0.6640  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

m3.bio <- glm(Ephedra.biomass~Density *Lvl, data=subset(clip, Ephedra.biomass>0), family=Gamma)
anova(m3.bio, test="Chisq")

## Analysis of Deviance Table
## 
## Model: Gamma, link: inverse
## 
## Response: Ephedra.biomass
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)    
## NULL                          106     48.613             
## Density      1   0.6174       105     47.996   0.1774    
## Lvl          2   9.2947       103     38.701 1.13e-06 ***
## Density:Lvl  2   0.9905       101     37.711   0.2324    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

m4 <-  glm(ephedra.end~brome.begin, data=recruit, family=binomial)
anova(m4, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: ephedra.end
## 
## Terms added sequentially (first to last)
## 
## 
##             Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL                          699     901.37         
## brome.begin  1   2.0214       698     899.35   0.1551

m4.bio <-  glm(Ephedra.biomass~brome.begin, data=subset(recruit, Ephedra.biomass>0 ), family=Gamma)
anova(m4.bio, test="Chisq")

## Analysis of Deviance Table
## 
## Model: Gamma, link: inverse
## 
## Response: Ephedra.biomass
## 
## Terms added sequentially (first to last)
## 
## 
##             Df  Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL                           209     89.330         
## brome.begin  1 0.0012905       208     89.328    0.953

## brome comparisons
library(lme4)

## Loading required package: Matrix

## 
## Attaching package: 'Matrix'

## The following objects are masked from 'package:tidyr':
## 
##     expand, pack, unpack

## Water
m1 <- glm(brome.begin/Density~ Lvl, weights=Density, data=subset(water, Density>0), family=binomial)
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: brome.begin/Density
## 
## Terms added sequentially (first to last)
## 
## 
##      Df Deviance Resid. Df Resid. Dev Pr(>Chi)   
## NULL                   239     475.39            
## Lvl   2   10.831       237     464.56 0.004447 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Shade
m2 <- glm(brome.begin/Density~ Lvl, weights=Density, data=subset(shade, Density>0), family=binomial)
anova(m2, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: brome.begin/Density
## 
## Terms added sequentially (first to last)
## 
## 
##      Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                   239     429.07              
## Lvl   2   31.496       237     397.57 1.448e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Clipping
m3<- glm(brome.begin/Density~ Lvl, weights=Density, data=subset(clip, Density>0), family=binomial)
anova(m3, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: brome.begin/Density
## 
## Terms added sequentially (first to last)
## 
## 
##      Df Deviance Resid. Df Resid. Dev Pr(>Chi)  
## NULL                   239     528.32           
## Lvl   2    8.962       237     519.35  0.01132 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Brome density vs Ephedra

dense <- recruit %>% filter(Ephedra.biomass>0) %>%  group_by(brome.begin) %>% summarize(bio=mean(Ephedra.biomass), recruit=mean(ephedra.end), germ=mean(ephedra.begin), abv.grd=mean(Ephedra.above),blw.grd=mean(Ephedra.below))

ggplot(dense, aes(x=brome.begin, y=bio))+geom_point()+ theme_Publication() +ylab("E. californica biomass") + xlab("brome density") + geom_smooth(method=lm, formula= y ~ poly(x,2))

## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

m1 <- lm(bio~poly(brome.begin,2), data=dense)

## recruitment no effect
ggplot(dense, aes(x=brome.begin, y=recruit))+geom_point()+ theme_Publication() +ylab("E. californica biomass") + xlab("brome density") #+ geom_smooth(method=lm, formula= y ~ x)

## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

m2 <- lm(recruit~brome.begin, data=dense)

## germination no effect
ggplot(dense, aes(x=brome.begin, y=germ))+geom_point()+ theme_Publication() +ylab("E. californica biomass") + xlab("brome density") #+ geom_smooth(method=lm, formula= y ~ x)

## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

m3 <- lm(germ~brome.begin, data=dense)


## above ground biomass 
ggplot(dense, aes(x=brome.begin, y=abv.grd))+geom_point()+ theme_Publication() +ylab("above-ground biomass") + xlab(expression(italic("B. madritensis")*" density")) + geom_smooth(method=lm, formula= y ~ x)+ xlim(0,20)

## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

m4 <- lm(abv.grd~brome.begin, data=dense)
summary(m4)

## 
## Call:
## lm(formula = abv.grd ~ brome.begin, data = dense)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.011652 -0.004168 -0.001584  0.002695  0.014099 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.0340643  0.0034082   9.995  9.4e-08 ***
## brome.begin -0.0007295  0.0003824  -1.908   0.0772 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.007214 on 14 degrees of freedom
## Multiple R-squared:  0.2063, Adjusted R-squared:  0.1496 
## F-statistic: 3.639 on 1 and 14 DF,  p-value: 0.07717

## below ground biomass
ggplot(dense, aes(x=brome.begin, y=blw.grd))+geom_point()+ theme_Publication() +ylab("below-ground biomass") + xlab(expression(italic("B. madritensis")*" density")) + geom_smooth(method=lm, formula= y ~ poly(x,2)) + xlim(0,20)

## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
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m5 <- lm(blw.grd~poly(brome.begin,2), data=dense)
summary(m5)

## 
## Call:
## lm(formula = blw.grd ~ poly(brome.begin, 2), data = dense)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0014710 -0.0007298 -0.0001058  0.0005620  0.0015789 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            0.0049697  0.0002432   20.44 2.89e-11 ***
## poly(brome.begin, 2)1 -0.0036473  0.0009726   -3.75  0.00243 ** 
## poly(brome.begin, 2)2 -0.0032968  0.0009726   -3.39  0.00484 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0009726 on 13 degrees of freedom
## Multiple R-squared:  0.6628, Adjusted R-squared:  0.6109 
## F-statistic: 12.78 on 2 and 13 DF,  p-value: 0.0008538

Compare regression co-efficients

library(broom)
recruit[is.na(recruit)] <- 0

## unique test
recruit[,"test"] <- paste0(recruit$Treatment,"-", recruit$Lvl)
biomass <- recruit %>% filter(Ephedra.biomass  > 0)

## join above and below
biolong <- biomass %>% gather(biomass, value, 14:15)

## conduct linear regression against brome density
regdata <- biolong %>% group_by(test, biomass) %>%
  do(lmOut = lm(log(value+0.0001) ~ poly(Density,2), data = .))
regcoef <- tidy(regdata, lmOut) %>% data.frame(.)  %>%  filter(term != "(Intercept)")
regcoef

##             test       biomass              term    estimate std.error
## 1   clipped-once Ephedra.above poly(Density, 2)1  0.27481615 0.6500371
## 2   clipped-once Ephedra.above poly(Density, 2)2 -0.14744877 0.6500371
## 3   clipped-once Ephedra.below poly(Density, 2)1  0.04790895 0.6388036
## 4   clipped-once Ephedra.below poly(Density, 2)2 -0.28040085 0.6388036
## 5  clipped-twice Ephedra.above poly(Density, 2)1 -0.78009563 0.6431364
## 6  clipped-twice Ephedra.above poly(Density, 2)2  1.07444554 0.6431364
## 7  clipped-twice Ephedra.below poly(Density, 2)1 -1.92114529 1.0557950
## 8  clipped-twice Ephedra.below poly(Density, 2)2 -1.12703841 1.0557950
## 9   control-none Ephedra.above poly(Density, 2)1 -2.41688646 1.0951954
## 10  control-none Ephedra.above poly(Density, 2)2 -1.63307394 1.0951954
## 11  control-none Ephedra.below poly(Density, 2)1 -0.87529650 1.1265107
## 12  control-none Ephedra.below poly(Density, 2)2 -1.45749959 1.1265107
## 13    shade-high Ephedra.above poly(Density, 2)1 -0.31628449 0.5460872
## 14    shade-high Ephedra.above poly(Density, 2)2 -0.34996609 0.5460872
## 15    shade-high Ephedra.below poly(Density, 2)1  0.04497215 0.7463155
## 16    shade-high Ephedra.below poly(Density, 2)2 -0.63676727 0.7463155
## 17     shade-med Ephedra.above poly(Density, 2)1 -0.43816008 0.7630626
## 18     shade-med Ephedra.above poly(Density, 2)2  0.07223617 0.7630626
## 19     shade-med Ephedra.below poly(Density, 2)1  0.69814968 0.7879161
## 20     shade-med Ephedra.below poly(Density, 2)2  0.09286347 0.7879161
## 21    water-high Ephedra.above poly(Density, 2)1  0.70269145 0.7806290
## 22    water-high Ephedra.above poly(Density, 2)2  0.25087933 0.7806290
## 23    water-high Ephedra.below poly(Density, 2)1 -0.22801320 1.1941965
## 24    water-high Ephedra.below poly(Density, 2)2 -1.11860350 1.1941965
## 25     water-low Ephedra.above poly(Density, 2)1  0.59110674 0.6219097
## 26     water-low Ephedra.above poly(Density, 2)2 -0.02386899 0.6219097
## 27     water-low Ephedra.below poly(Density, 2)1 -1.26964812 1.1063110
## 28     water-low Ephedra.below poly(Density, 2)2 -1.08669728 1.1063110
##      statistic    p.value
## 1   0.42276995 0.67558161
## 2  -0.22683131 0.82214630
## 3   0.07499793 0.94073133
## 4  -0.43894689 0.66395317
## 5  -1.21295525 0.23304633
## 6   1.67063411 0.10346703
## 7  -1.81961969 0.07714106
## 8  -1.06747850 0.29286225
## 9  -2.20680834 0.03439420
## 10 -1.49112557 0.14542654
## 11 -0.77699792 0.44269442
## 12 -1.29381775 0.20471093
## 13 -0.57918309 0.57106186
## 14 -0.64086116 0.53128268
## 15  0.06025890 0.95274496
## 16 -0.85321458 0.40695901
## 17 -0.57421247 0.57737725
## 18  0.09466611 0.92628248
## 19  0.88607106 0.39453765
## 20  0.11785958 0.90830350
## 21  0.90016063 0.37418692
## 22  0.32138102 0.74983309
## 23 -0.19093441 0.84968025
## 24 -0.93669973 0.35533185
## 25  0.95047037 0.34946828
## 26 -0.03838015 0.96963886
## 27 -1.14764120 0.26018664
## 28 -0.98227104 0.33382220

## compare root vs shoot linear-models only
regdata <- biolong %>% group_by(test, biomass) %>%
  do(lmOut = lm(log(value+0.0001) ~ Density -1, data = .))
regcoef <- tidy(regdata, lmOut) %>% data.frame(.)  %>%  filter(term != "(Intercept)")
regcoef

##             test       biomass    term   estimate  std.error statistic
## 1   clipped-once Ephedra.above Density -0.2626104 0.04651326 -5.645926
## 2   clipped-once Ephedra.below Density -0.3696163 0.06326839 -5.842037
## 3  clipped-twice Ephedra.above Density -0.2941285 0.05045686 -5.829307
## 4  clipped-twice Ephedra.below Density -0.4189320 0.06924742 -6.049785
## 5   control-none Ephedra.above Density -0.3283941 0.05086589 -6.456077
## 6   control-none Ephedra.below Density -0.4483319 0.07767200 -5.772117
## 7     shade-high Ephedra.above Density -0.2433404 0.05849616 -4.159938
## 8     shade-high Ephedra.below Density -0.3750912 0.09368469 -4.003762
## 9      shade-med Ephedra.above Density -0.2579739 0.05442674 -4.739838
## 10     shade-med Ephedra.below Density -0.3667645 0.08642932 -4.243520
## 11    water-high Ephedra.above Density -0.2273466 0.04499472 -5.052740
## 12    water-high Ephedra.below Density -0.3611560 0.06632018 -5.445642
## 13     water-low Ephedra.above Density -0.2492054 0.04295041 -5.802165
## 14     water-low Ephedra.below Density -0.4236047 0.06414468 -6.603895
##         p.value
## 1  3.371231e-06
## 2  1.924762e-06
## 3  9.761705e-07
## 4  4.864409e-07
## 5  1.945196e-07
## 6  1.541832e-06
## 7  6.559799e-04
## 8  9.196789e-04
## 9  3.864364e-04
## 10 9.586756e-04
## 11 1.198334e-05
## 12 3.536915e-06
## 13 1.926020e-06
## 14 1.912173e-07

## Test above vs below response to brome on density gradient
t.test(estimate ~ biomass, data=regcoef)

## 
##  Welch Two Sample t-test
## 
## data:  estimate by biomass
## t = 6.9796, df = 11.998, p-value = 1.477e-05
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.08848354 0.16880138
## sample estimates:
## mean in group Ephedra.above mean in group Ephedra.below 
##                  -0.2661428                  -0.3947852

## Check against brome Biomass
regdata <- biolong %>% group_by(test, biomass) %>%
  do(lmOut = lm(log(value+0.0001) ~ brome.biomass -1 , data = .))
biolong %>% group_by(test, biomass) %>% summarize(n=length(value))

## # A tibble: 14 x 3
## # Groups:   test [7]
##    test          biomass           n
##    <chr>         <chr>         <int>
##  1 clipped-once  Ephedra.above    32
##  2 clipped-once  Ephedra.below    32
##  3 clipped-twice Ephedra.above    39
##  4 clipped-twice Ephedra.below    39
##  5 control-none  Ephedra.above    36
##  6 control-none  Ephedra.below    36
##  7 shade-high    Ephedra.above    18
##  8 shade-high    Ephedra.below    18
##  9 shade-med     Ephedra.above    14
## 10 shade-med     Ephedra.below    14
## 11 water-high    Ephedra.above    38
## 12 water-high    Ephedra.below    38
## 13 water-low     Ephedra.above    33
## 14 water-low     Ephedra.below    33

regcoef <- tidy(regdata, lmOut, n) %>% data.frame(.)  %>%  filter(term != "(Intercept)")
regcoef

##             test       biomass          term   estimate std.error statistic
## 1   clipped-once Ephedra.above brome.biomass -13.385395 1.6020711 -8.355057
## 2   clipped-once Ephedra.below brome.biomass -18.346804 2.2665821 -8.094480
## 3  clipped-twice Ephedra.above brome.biomass -18.029511 3.1979346 -5.637861
## 4  clipped-twice Ephedra.below brome.biomass -25.726637 4.3868000 -5.864557
## 5   control-none Ephedra.above brome.biomass  -8.229579 1.4216487 -5.788757
## 6   control-none Ephedra.below brome.biomass -12.784337 1.8838040 -6.786447
## 7     shade-high Ephedra.above brome.biomass  -9.344363 3.0416655 -3.072120
## 8     shade-high Ephedra.below brome.biomass -14.371476 4.8356921 -2.971958
## 9      shade-med Ephedra.above brome.biomass -11.845188 2.6007340 -4.554556
## 10     shade-med Ephedra.below brome.biomass -16.181929 4.3086956 -3.755645
## 11    water-high Ephedra.above brome.biomass  -1.636745 0.3202788 -5.110377
## 12    water-high Ephedra.below brome.biomass  -2.517458 0.4836808 -5.204793
## 13     water-low Ephedra.above brome.biomass  -3.151942 0.6876007 -4.583972
## 14     water-low Ephedra.below brome.biomass  -5.063517 1.1001728 -4.602474
##         p.value
## 1  1.944844e-09
## 2  3.848959e-09
## 3  1.787076e-06
## 4  8.732890e-07
## 5  1.465849e-06
## 6  7.219249e-08
## 7  6.904691e-03
## 8  8.550531e-03
## 9  5.406319e-04
## 10 2.401544e-03
## 11 1.002474e-05
## 12 7.480114e-06
## 13 6.629695e-05
## 14 6.285306e-05

## Test root vs shoot
t.test(estimate ~ biomass, data=regcoef)

## 
##  Welch Two Sample t-test
## 
## data:  estimate by biomass
## t = 1.1387, df = 10.954, p-value = 0.2791
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -3.918299 12.309566
## sample estimates:
## mean in group Ephedra.above mean in group Ephedra.below 
##                   -9.374675                  -13.570308

## rename test column
newframe <- data.frame(test=unique(regcoef$test), treatments=c("clip-1", "clip-2","control","high shade","med shade","high water","low water"), sorting=c(2,3,1,5,4,7,6))  
newframe <- rbind(newframe, newframe)                   
newframe[,"biomass"]  <- rep(unique(regcoef$biomass), each=7) 
newframe[,"tissue"] <- rep(c("aboveground","belowground"), each=7)


coefplot <- merge(regcoef, newframe, by=c("test","biomass"))
coefplot[order(coefplot$sorting),]

##             test       biomass          term   estimate std.error statistic
## 5   control-none Ephedra.above brome.biomass  -8.229579 1.4216487 -5.788757
## 6   control-none Ephedra.below brome.biomass -12.784337 1.8838040 -6.786447
## 1   clipped-once Ephedra.above brome.biomass -13.385395 1.6020711 -8.355057
## 2   clipped-once Ephedra.below brome.biomass -18.346804 2.2665821 -8.094480
## 3  clipped-twice Ephedra.above brome.biomass -18.029511 3.1979346 -5.637861
## 4  clipped-twice Ephedra.below brome.biomass -25.726637 4.3868000 -5.864557
## 9      shade-med Ephedra.above brome.biomass -11.845188 2.6007340 -4.554556
## 10     shade-med Ephedra.below brome.biomass -16.181929 4.3086956 -3.755645
## 7     shade-high Ephedra.above brome.biomass  -9.344363 3.0416655 -3.072120
## 8     shade-high Ephedra.below brome.biomass -14.371476 4.8356921 -2.971958
## 13     water-low Ephedra.above brome.biomass  -3.151942 0.6876007 -4.583972
## 14     water-low Ephedra.below brome.biomass  -5.063517 1.1001728 -4.602474
## 11    water-high Ephedra.above brome.biomass  -1.636745 0.3202788 -5.110377
## 12    water-high Ephedra.below brome.biomass  -2.517458 0.4836808 -5.204793
##         p.value treatments sorting      tissue
## 5  1.465849e-06    control       1 aboveground
## 6  7.219249e-08    control       1 belowground
## 1  1.944844e-09     clip-1       2 aboveground
## 2  3.848959e-09     clip-1       2 belowground
## 3  1.787076e-06     clip-2       3 aboveground
## 4  8.732890e-07     clip-2       3 belowground
## 9  5.406319e-04  med shade       4 aboveground
## 10 2.401544e-03  med shade       4 belowground
## 7  6.904691e-03 high shade       5 aboveground
## 8  8.550531e-03 high shade       5 belowground
## 13 6.629695e-05  low water       6 aboveground
## 14 6.285306e-05  low water       6 belowground
## 11 1.002474e-05 high water       7 aboveground
## 12 7.480114e-06 high water       7 belowground

coefplot$treatments <- reorder(coefplot$treatments, coefplot$sorting)

## plot regression coefficients
ggplot(coefplot, aes(x=treatments, y=estimate)) + geom_point(size=3) + facet_grid(~tissue) + theme_Publication() + geom_errorbar(aes(x=treatments, ymin=estimate-std.error, ymax=estimate+std.error), width=0) + xlab("") + ylab("B. madritnesis effect")

## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

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## plot raw biomass among treatments
bioavg <- biolong %>% group_by(test, biomass) %>% summarize(bio=mean(value), error=se(value))
bioavg <- merge(bioavg, newframe)

bioavg$treatments <- reorder(bioavg$treatments, bioavg$sorting)

ggplot(bioavg, aes(x=treatments, y=bio, fill=tissue)) + geom_bar(stat="identity", position=position_dodge(width=0.9), color="black") + ylab("biomass (g)") + theme_Publication() + geom_errorbar(aes(x=treatments, ymin=bio-error, ymax=bio+error), position=position_dodge(width=0.9), width=0) + xlab("") + scale_fill_brewer()

## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing

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ANCOVA and probability of establishment

## unique test
recruit[,"test"] <- paste0(recruit$Treatment,"-", recruit$Lvl)
recruit[is.na(recruit)] <- 0
biomass <- recruit %>% filter(Ephedra.biomass  > 0 & Ephedra.biomass < 0.6)


library(emmeans)


## Compare Emergence
m1 <- glm(ephedra.begin ~ Density* test, data=recruit, family="binomial")
anova(m1, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: ephedra.begin
## 
## Terms added sequentially (first to last)
## 
## 
##              Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                           699     965.59              
## Density       1   3.5657       698     962.03   0.05898 .  
## test          6  30.5072       692     931.52 3.147e-05 ***
## Density:test  6   6.4480       686     925.07   0.37492    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

emmeans(m1, pairwise~test, var="ephedra.begin")

## NOTE: Results may be misleading due to involvement in interactions

## $emmeans
##  test          emmean    SE  df asymp.LCL asymp.UCL
##  clipped-once  -0.120 0.201 Inf   -0.5135    0.2727
##  clipped-twice -0.286 0.203 Inf   -0.6849    0.1125
##  control-none   0.201 0.201 Inf   -0.1933    0.5951
##  shade-high    -0.490 0.206 Inf   -0.8936   -0.0858
##  shade-med     -1.061 0.249 Inf   -1.5487   -0.5740
##  water-high     0.493 0.207 Inf    0.0876    0.8992
##  water-low     -0.080 0.200 Inf   -0.4723    0.3123
## 
## Results are given on the logit (not the response) scale. 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast                     estimate    SE  df z.ratio p.value
##  clipped-once - clipped-twice   0.1658 0.286 Inf  0.580  0.9974 
##  clipped-once - control-none   -0.3213 0.284 Inf -1.131  0.9186 
##  clipped-once - shade-high      0.3693 0.288 Inf  1.284  0.8595 
##  clipped-once - shade-med       0.9409 0.319 Inf  2.945  0.0504 
##  clipped-once - water-high     -0.6138 0.288 Inf -2.129  0.3352 
##  clipped-once - water-low      -0.0404 0.283 Inf -0.143  1.0000 
##  clipped-twice - control-none  -0.4871 0.286 Inf -1.703  0.6142 
##  clipped-twice - shade-high     0.2035 0.290 Inf  0.703  0.9925 
##  clipped-twice - shade-med      0.7751 0.321 Inf  2.413  0.1930 
##  clipped-twice - water-high    -0.7796 0.290 Inf -2.686  0.1017 
##  clipped-twice - water-low     -0.2062 0.285 Inf -0.723  0.9913 
##  control-none - shade-high      0.6906 0.288 Inf  2.398  0.1991 
##  control-none - shade-med       1.2623 0.320 Inf  3.947  0.0015 
##  control-none - water-high     -0.2925 0.289 Inf -1.013  0.9512 
##  control-none - water-low       0.2809 0.284 Inf  0.990  0.9563 
##  shade-high - shade-med         0.5717 0.323 Inf  1.770  0.5683 
##  shade-high - water-high       -0.9831 0.292 Inf -3.365  0.0135 
##  shade-high - water-low        -0.4096 0.287 Inf -1.426  0.7879 
##  shade-med - water-high        -1.5547 0.324 Inf -4.805  <.0001 
##  shade-med - water-low         -0.9813 0.319 Inf -3.074  0.0344 
##  water-high - water-low         0.5734 0.288 Inf  1.991  0.4202 
## 
## Results are given on the log odds ratio (not the response) scale. 
## P value adjustment: tukey method for comparing a family of 7 estimates

## Compare Establishment
m2 <- glm(ephedra.end ~ Density* test, data=recruit, family="binomial")
anova(m2, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: ephedra.end
## 
## Terms added sequentially (first to last)
## 
## 
##              Df Deviance Resid. Df Resid. Dev Pr(>Chi)  
## NULL                           699     901.37           
## Density       1   4.9171       698     896.46  0.02659 *
## test          6  16.2032       692     880.25  0.01270 *
## Density:test  6   2.9002       686     877.35  0.82127  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

emmeans(m2, pairwise~test, var="ephedra.end")

## NOTE: Results may be misleading due to involvement in interactions

## $emmeans
##  test          emmean    SE  df asymp.LCL asymp.UCL
##  clipped-once  -0.666 0.212 Inf    -1.081   -0.2512
##  clipped-twice -0.469 0.210 Inf    -0.881   -0.0568
##  control-none  -0.583 0.210 Inf    -0.994   -0.1712
##  shade-high    -0.533 0.207 Inf    -0.939   -0.1267
##  shade-med     -1.539 0.266 Inf    -2.060   -1.0182
##  water-high    -0.454 0.207 Inf    -0.859   -0.0489
##  water-low     -0.493 0.207 Inf    -0.898   -0.0873
## 
## Results are given on the logit (not the response) scale. 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast                     estimate    SE  df z.ratio p.value
##  clipped-once - clipped-twice  -0.1974 0.298 Inf -0.662  0.9946 
##  clipped-once - control-none   -0.0833 0.298 Inf -0.279  1.0000 
##  clipped-once - shade-high     -0.1331 0.296 Inf -0.449  0.9994 
##  clipped-once - shade-med       0.8730 0.340 Inf  2.569  0.1354 
##  clipped-once - water-high     -0.2121 0.296 Inf -0.717  0.9916 
##  clipped-once - water-low      -0.1736 0.296 Inf -0.587  0.9972 
##  clipped-twice - control-none   0.1141 0.297 Inf  0.384  0.9998 
##  clipped-twice - shade-high     0.0643 0.295 Inf  0.218  1.0000 
##  clipped-twice - shade-med      1.0704 0.339 Inf  3.159  0.0265 
##  clipped-twice - water-high    -0.0147 0.295 Inf -0.050  1.0000 
##  clipped-twice - water-low      0.0238 0.295 Inf  0.081  1.0000 
##  control-none - shade-high     -0.0498 0.295 Inf -0.169  1.0000 
##  control-none - shade-med       0.9563 0.339 Inf  2.823  0.0709 
##  control-none - water-high     -0.1288 0.295 Inf -0.437  0.9995 
##  control-none - water-low      -0.0903 0.295 Inf -0.306  0.9999 
##  shade-high - shade-med         1.0061 0.337 Inf  2.985  0.0449 
##  shade-high - water-high       -0.0790 0.293 Inf -0.270  1.0000 
##  shade-high - water-low        -0.0405 0.293 Inf -0.138  1.0000 
##  shade-med - water-high        -1.0851 0.337 Inf -3.223  0.0216 
##  shade-med - water-low         -1.0466 0.337 Inf -3.108  0.0310 
##  water-high - water-low         0.0385 0.292 Inf  0.132  1.0000 
## 
## Results are given on the log odds ratio (not the response) scale. 
## P value adjustment: tukey method for comparing a family of 7 estimates

## Compare growth
m3 <- lm(sqrt(Ephedra.above+0.001) ~ test * brome.biomass, data=biomass)
anova(m3)

## Analysis of Variance Table
## 
## Response: sqrt(Ephedra.above + 0.001)
##                     Df  Sum Sq   Mean Sq F value    Pr(>F)    
## test                 6 0.11764 0.0196070  8.1532 7.038e-08 ***
## brome.biomass        1 0.00040 0.0003956  0.1645   0.68547    
## test:brome.biomass   6 0.03015 0.0050243  2.0893   0.05613 .  
## Residuals          196 0.47134 0.0024048                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## compare pairwise comparisons
interact <- lstrends(m3,  ~ test , var = "brome.biomass")
contrast(interact,         list("clipped"=c(.5,.5,-1,0,0,0,0),"shade"=c(0,0,-1,.5,.5,0,0),"water"=c(0,0,-1,0,0,.5,.5)))

## Note: Use 'contrast(regrid(object), ...)' to obtain contrasts of back-transformed estimates

##  contrast estimate     SE  df t.ratio p.value
##  clipped   -0.0718 0.0607 196 -1.182  0.2386 
##  shade     -0.1604 0.0625 196 -2.568  0.0110 
##  water     -0.0639 0.0406 196 -1.574  0.1171 
## 
## Note: contrasts are still on the 0.001(mu + 0.001) scale

## Model below
m4 <- lm(sqrt(Ephedra.below+0.001) ~ test * brome.biomass, data=biomass)
anova(m4)

## Analysis of Variance Table
## 
## Response: sqrt(Ephedra.below + 0.001)
##                     Df   Sum Sq    Mean Sq F value    Pr(>F)    
## test                 6 0.012375 0.00206250  3.9241 0.0009997 ***
## brome.biomass        1 0.000006 0.00000634  0.0121 0.9126479    
## test:brome.biomass   6 0.002439 0.00040654  0.7735 0.5916155    
## Residuals          196 0.103017 0.00052560                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Germination patterns

recruit

##      ID Treatment   Lvl Rep Density ephedra.emergence branching fluoro
## 1     5   clipped  once   1       0                 0         0 0.0000
## 2    10   clipped  once   2       0                 1         2 0.3215
## 3    13   clipped  once   3       0                 1         6 0.7433
## 4    17   clipped  once   4       0                 0         0 0.0000
## 5    23   clipped  once   5       0                 0         0 0.0000
## 6    26   clipped  once   6       0                 0         0 0.0000
## 7    35   clipped  once   7       0                 0         0 0.0000
## 8    39   clipped  once   8       0                 1         4 0.6366
## 9    44   clipped  once   9       0                 0         0 0.0000
## 10   48   clipped  once  10       0                 0         0 0.0000
## 11   53   clipped  once  11       0                 2         8 0.7806
## 12   56   clipped  once  12       0                 0         0 0.0000
## 13   64   clipped  once  13       0                 0         0 0.0000
## 14   69   clipped  once  14       0                 0         0 0.0000
## 15   74   clipped  once  15       0                 0         0 0.0000
## 16   76   clipped  once  16       0                 0         0 0.0000
## 17   81   clipped  once  17       0                 0         0 0.0000
## 18   86   clipped  once  18       0                 0         0 0.0000
## 19   92   clipped  once  19       0                 0         0 0.0000
## 20   96   clipped  once  20       0                 0         0 0.0000
## 21  105   clipped twice   1       0                 0         0 0.0000
## 22  110   clipped twice   2       0                 1         8 0.7619
## 23  113   clipped twice   3       0                 1         5 0.8012
## 24  117   clipped twice   4       0                 1         4 0.7447
## 25  123   clipped twice   5       0                 2         5 0.7471
## 26  126   clipped twice   6       0                 0         0 0.0000
## 27  135   clipped twice   7       0                 1         4 0.5985
## 28  139   clipped twice   8       0                 1         5 0.7935
## 29  144   clipped twice   9       0                 0         0 0.0000
## 30  148   clipped twice  10       0                 1         6 0.6318
## 31  153   clipped twice  11       0                 1         6 0.6807
## 32  156   clipped twice  12       0                 0         0 0.0000
## 33  164   clipped twice  13       0                 0         0 0.0000
## 34  169   clipped twice  14       0                 0         0 0.0000
## 35  174   clipped twice  15       0                 0         0 0.0000
## 36  176   clipped twice  16       0                 1         4 0.7650
## 37  181   clipped twice  17       0                 0         0 0.0000
## 38  186   clipped twice  18       0                 0         0 0.0000
## 39  192   clipped twice  19       0                 0         0 0.0000
## 40  196   clipped twice  20       0                 0         0 0.0000
## 41    4   clipped  once   1       2                 0         0 0.0000
## 42    9   clipped  once   2       2                 0         0 0.0000
## 43   15   clipped  once   3       2                 0         0 0.0000
## 44   20   clipped  once   4       2                 0         0 0.0000
## 45   21   clipped  once   5       2                 0         0 0.0000
## 46   28   clipped  once   6       2                 0         0 0.0000
## 47   34   clipped  once   7       2                 0         0 0.0000
## 48   38   clipped  once   8       2                 0         0 0.0000
## 49   42   clipped  once   9       2                 0         0 0.0000
## 50   47   clipped  once  10       2                 0         0 0.0000
## 51   52   clipped  once  11       2                 0         0 0.0000
## 52   60   clipped  once  12       2                 0         0 0.0000
## 53   63   clipped  once  13       2                 0         0 0.0000
## 54   70   clipped  once  14       2                 0         0 0.0000
## 55   71   clipped  once  15       2                 1         6 0.7615
## 56   80   clipped  once  16       2                 2         7 0.7943
## 57   83   clipped  once  17       2                 0         0 0.0000
## 58   88   clipped  once  18       2                 0         0 0.0000
## 59   91   clipped  once  19       2                 0         0 0.0000
## 60   98   clipped  once  20       2                 0         0 0.0000
## 61  104   clipped twice   1       2                 1         6 0.6954
## 62  109   clipped twice   2       2                 0         0 0.0000
## 63  115   clipped twice   3       2                 1         4 0.7570
## 64  120   clipped twice   4       2                 0         0 0.0000
## 65  121   clipped twice   5       2                 0         0 0.0000
## 66  128   clipped twice   6       2                 0         0 0.0000
## 67  134   clipped twice   7       2                 0         0 0.0000
## 68  138   clipped twice   8       2                 0         0 0.0000
## 69  142   clipped twice   9       2                 0         0 0.0000
## 70  147   clipped twice  10       2                 0         0 0.0000
## 71  152   clipped twice  11       2                 1         4 0.7681
## 72  160   clipped twice  12       2                 0         0 0.0000
## 73  163   clipped twice  13       2                 0         0 0.0000
## 74  170   clipped twice  14       2                 1         6 0.7063
## 75  171   clipped twice  15       2                 0         0 0.0000
## 76  180   clipped twice  16       2                 1         4 0.7995
## 77  183   clipped twice  17       2                 0         0 0.0000
## 78  188   clipped twice  18       2                 0         0 0.0000
## 79  191   clipped twice  19       2                 0         0 0.0000
## 80  198   clipped twice  20       2                 0         0 0.0000
## 81    3   clipped  once   1       5                 1         3 0.6416
## 82    8   clipped  once   2       5                 0         0 0.0000
## 83   14   clipped  once   3       5                 1         4 0.7920
## 84   18   clipped  once   4       5                 0         0 0.0000
## 85   22   clipped  once   5       5                 0         0 0.0000
## 86   29   clipped  once   6       5                 1         5 0.6169
## 87   32   clipped  once   7       5                 0         0 0.0000
## 88   40   clipped  once   8       5                 1         4 0.6732
## 89   41   clipped  once   9       5                 2         8 0.7775
## 90   49   clipped  once  10       5                 1         5 0.8054
## 91   54   clipped  once  11       5                 2         4 0.7938
## 92   59   clipped  once  12       5                 1         3 0.7967
## 93   62   clipped  once  13       5                 1         5 0.7612
## 94   66   clipped  once  14       5                 1         6 0.7740
## 95   73   clipped  once  15       5                 1        11 0.7853
## 96   77   clipped  once  16       5                 0         0 0.0000
## 97   85   clipped  once  17       5                 0         0 0.0000
## 98   87   clipped  once  18       5                 1         6 0.7532
## 99   95   clipped  once  19       5                 0         0 0.0000
## 100  97   clipped  once  20       5                 1         5 0.7839
## 101 103   clipped twice   1       5                 2         6 0.7245
## 102 108   clipped twice   2       5                 2         6 0.7800
## 103 114   clipped twice   3       5                 0         0 0.0000
## 104 118   clipped twice   4       5                 0         0 0.0000
## 105 122   clipped twice   5       5                 1         4 0.7698
## 106 129   clipped twice   6       5                 0         0 0.0000
## 107 132   clipped twice   7       5                 1         6 0.7884
## 108 140   clipped twice   8       5                 0         0 0.0000
## 109 141   clipped twice   9       5                 0         0 0.0000
## 110 149   clipped twice  10       5                 0         0 0.0000
## 111 154   clipped twice  11       5                 0         0 0.0000
## 112 159   clipped twice  12       5                 0         0 0.0000
## 113 162   clipped twice  13       5                 1         4 0.4452
## 114 166   clipped twice  14       5                 1         7 0.6691
## 115 173   clipped twice  15       5                 0         0 0.0000
## 116 177   clipped twice  16       5                 0         0 0.0000
## 117 185   clipped twice  17       5                 1         4 0.7774
## 118 187   clipped twice  18       5                 0         0 0.0000
## 119 195   clipped twice  19       5                 1         5 0.7694
## 120 197   clipped twice  20       5                 1         4 0.7631
## 121   1   clipped  once   1      10                 1         6 0.7867
## 122   6   clipped  once   2      10                 1         3 0.7592
## 123  12   clipped  once   3      10                 0         0 0.0000
## 124  16   clipped  once   4      10                 0         0 0.0000
## 125  25   clipped  once   5      10                 0         0 0.0000
## 126  27   clipped  once   6      10                 0         0 0.0000
## 127  33   clipped  once   7      10                 1         5 0.7789
## 128  36   clipped  once   8      10                 1         7 0.7092
## 129  43   clipped  once   9      10                 0         0 0.0000
## 130  50   clipped  once  10      10                 0         0 0.0000
## 131  55   clipped  once  11      10                 1         4 0.6851
## 132  58   clipped  once  12      10                 0         0 0.0000
## 133  65   clipped  once  13      10                 0         0 0.0000
## 134  68   clipped  once  14      10                 0         0 0.0000
## 135  75   clipped  once  15      10                 1         4 0.7576
## 136  78   clipped  once  16      10                 1         8 0.7499
## 137  84   clipped  once  17      10                 0         0 0.0000
## 138  90   clipped  once  18      10                 0         0 0.0000
## 139  93   clipped  once  19      10                 0         0 0.0000
## 140  99   clipped  once  20      10                 0         0 0.0000
## 141 101   clipped twice   1      10                 0         0 0.0000
## 142 106   clipped twice   2      10                 1         6 0.7842
## 143 112   clipped twice   3      10                 0         0 0.0000
## 144 116   clipped twice   4      10                 0         0 0.0000
## 145 125   clipped twice   5      10                 0         0 0.0000
## 146 127   clipped twice   6      10                 1         5 0.7753
## 147 133   clipped twice   7      10                 0         0 0.0000
## 148 136   clipped twice   8      10                 0         0 0.0000
## 149 143   clipped twice   9      10                 0         0 0.0000
## 150 150   clipped twice  10      10                 1         5 0.7420
## 151 155   clipped twice  11      10                 0         0 0.0000
## 152 158   clipped twice  12      10                 2         7 0.7999
## 153 165   clipped twice  13      10                 0         0 0.0000
## 154 168   clipped twice  14      10                 3         9 0.6319
## 155 175   clipped twice  15      10                 0         0 0.0000
## 156 178   clipped twice  16      10                 2         5 0.5698
## 157 184   clipped twice  17      10                 0         0 0.0000
## 158 190   clipped twice  18      10                 1         4 0.7780
## 159 193   clipped twice  19      10                 0         0 0.0000
## 160 199   clipped twice  20      10                 0         0 0.0000
## 161   2   clipped  once   1      20                 1         7 0.7863
## 162   7   clipped  once   2      20                 0         0 0.0000
## 163  11   clipped  once   3      20                 0         0 0.0000
## 164  19   clipped  once   4      20                 0         0 0.0000
## 165  24   clipped  once   5      20                 0         0 0.0000
## 166  30   clipped  once   6      20                 0         0 0.0000
## 167  31   clipped  once   7      20                 0         0 0.0000
## 168  37   clipped  once   8      20                 0         0 0.0000
## 169  45   clipped  once   9      20                 0         0 0.0000
## 170  46   clipped  once  10      20                 0         0 0.0000
## 171  51   clipped  once  11      20                 0         0 0.0000
## 172  57   clipped  once  12      20                 0         0 0.0000
## 173  61   clipped  once  13      20                 0         0 0.0000
## 174  67   clipped  once  14      20                 0         0 0.0000
## 175  72   clipped  once  15      20                 0         0 0.0000
## 176  79   clipped  once  16      20                 0         0 0.0000
## 177  82   clipped  once  17      20                 0         0 0.0000
## 178  89   clipped  once  18      20                 0         0 0.0000
## 179  94   clipped  once  19      20                 0         0 0.0000
## 180 100   clipped  once  20      20                 1         4 0.6715
## 181 102   clipped twice   1      20                 0         0 0.0000
## 182 107   clipped twice   2      20                 0         0 0.0000
## 183 111   clipped twice   3      20                 0         0 0.0000
## 184 119   clipped twice   4      20                 0         0 0.0000
## 185 124   clipped twice   5      20                 0         0 0.0000
## 186 130   clipped twice   6      20                 1         5 0.5799
## 187 131   clipped twice   7      20                 0         0 0.0000
## 188 137   clipped twice   8      20                 0         0 0.0000
## 189 145   clipped twice   9      20                 1         3 0.7009
## 190 146   clipped twice  10      20                 0         0 0.0000
## 191 151   clipped twice  11      20                 1         5 0.7652
## 192 157   clipped twice  12      20                 0         0 0.0000
## 193 161   clipped twice  13      20                 0         0 0.0000
## 194 167   clipped twice  14      20                 0         0 0.0000
## 195 172   clipped twice  15      20                 0         0 0.0000
## 196 179   clipped twice  16      20                 0         0 0.0000
## 197 182   clipped twice  17      20                 2         6 0.7488
## 198 189   clipped twice  18      20                 0         0 0.0000
## 199 194   clipped twice  19      20                 0         0 0.0000
## 200 200   clipped twice  20      20                 0         0 0.0000
## 201 205   control  none   1       0                 0         0 0.0000
## 202 210   control  none   2       0                 0         0 0.0000
## 203 213   control  none   3       0                 1         5 0.7908
## 204 217   control  none   4       0                 1         3 0.7910
## 205 223   control  none   5       0                 0         0 0.0000
## 206 226   control  none   6       0                 0         0 0.0000
## 207 235   control  none   7       0                 1         6 0.7779
## 208 239   control  none   8       0                 0         0 0.0000
## 209 244   control  none   9       0                 1         6 0.5830
## 210 248   control  none  10       0                 1         5 0.7768
## 211 253   control  none  11       0                 0         0 0.0000
## 212 256   control  none  12       0                 0         0 0.0000
## 213 264   control  none  13       0                 0         0 0.0000
## 214 269   control  none  14       0                 0         0 0.0000
## 215 274   control  none  15       0                 0         0 0.0000
## 216 276   control  none  16       0                 1         4 0.7781
## 217 281   control  none  17       0                 0         0 0.0000
## 218 286   control  none  18       0                 0         0 0.0000
## 219 292   control  none  19       0                 0         0 0.0000
## 220 296   control  none  20       0                 0         0 0.0000
## 221 204   control  none   1       2                 1         9 0.6990
## 222 209   control  none   2       2                 0         0 0.0000
## 223 215   control  none   3       2                 0         0 0.0000
## 224 220   control  none   4       2                 0         0 0.0000
## 225 221   control  none   5       2                 0         0 0.0000
## 226 228   control  none   6       2                 0         0 0.0000
## 227 234   control  none   7       2                 1         5 0.7909
## 228 238   control  none   8       2                 0         0 0.0000
## 229 242   control  none   9       2                 1         5 0.7632
## 230 247   control  none  10       2                 0         0 0.0000
## 231 252   control  none  11       2                 1         7 0.8060
## 232 260   control  none  12       2                 1         7 0.7774
## 233 263   control  none  13       2                 0         0 0.0000
## 234 270   control  none  14       2                 0         0 0.0000
## 235 271   control  none  15       2                 1         6 0.7727
## 236 280   control  none  16       2                 0         0 0.0000
## 237 283   control  none  17       2                 2         5 0.7937
## 238 288   control  none  18       2                 0         0 0.0000
## 239 291   control  none  19       2                 1         3 0.4486
## 240 298   control  none  20       2                 0         0 0.0000
## 241 203   control  none   1       5                 0         0 0.0000
## 242 208   control  none   2       5                 0         0 0.0000
## 243 214   control  none   3       5                 0         0 0.0000
## 244 218   control  none   4       5                 0         0 0.0000
## 245 222   control  none   5       5                 0         0 0.0000
## 246 229   control  none   6       5                 1         6 0.8044
## 247 232   control  none   7       5                 1         3 0.8003
## 248 240   control  none   8       5                 0         0 0.0000
## 249 241   control  none   9       5                 1         3 0.4088
## 250 249   control  none  10       5                 0         0 0.0000
## 251 254   control  none  11       5                 0         0 0.0000
## 252 259   control  none  12       5                 0         0 0.0000
## 253 262   control  none  13       5                 1         9 0.7871
## 254 266   control  none  14       5                 2         5 0.7579
## 255 273   control  none  15       5                 0         0 0.0000
## 256 277   control  none  16       5                 1         3 0.7850
## 257 285   control  none  17       5                 2         8 0.7973
## 258 287   control  none  18       5                 0         0 0.0000
## 259 295   control  none  19       5                 1         5 0.7066
## 260 297   control  none  20       5                 0         0 0.0000
## 261 201   control  none   1      10                 0         0 0.0000
## 262 206   control  none   2      10                 1         5 0.7773
## 263 212   control  none   3      10                 0         0 0.0000
## 264 216   control  none   4      10                 0         0 0.0000
## 265 225   control  none   5      10                 0         0 0.0000
## 266 227   control  none   6      10                 1         7 0.7974
## 267 233   control  none   7      10                 2         3 0.6053
## 268 236   control  none   8      10                 0         0 0.0000
## 269 243   control  none   9      10                 0         0 0.0000
## 270 250   control  none  10      10                 0         0 0.0000
## 271 255   control  none  11      10                 2         7 0.7887
## 272 258   control  none  12      10                 0         0 0.0000
## 273 265   control  none  13      10                 0         0 0.0000
## 274 268   control  none  14      10                 0         0 0.0000
## 275 275   control  none  15      10                 1         7 0.7880
## 276 278   control  none  16      10                 0         0 0.0000
## 277 284   control  none  17      10                 1         4 0.7938
## 278 290   control  none  18      10                 0         0 0.0000
## 279 293   control  none  19      10                 0         0 0.0000
## 280 299   control  none  20      10                 0         0 0.0000
## 281 202   control  none   1      20                 1         3 0.7360
## 282 207   control  none   2      20                 1         5 0.7544
## 283 211   control  none   3      20                 0         0 0.0000
## 284 219   control  none   4      20                 0         0 0.0000
## 285 224   control  none   5      20                 0         0 0.0000
## 286 230   control  none   6      20                 0         0 0.0000
## 287 231   control  none   7      20                 2         5 0.6865
## 288 237   control  none   8      20                 1         3 0.7434
## 289 245   control  none   9      20                 0         0 0.0000
## 290 246   control  none  10      20                 0         0 0.0000
## 291 251   control  none  11      20                 0         0 0.0000
## 292 257   control  none  12      20                 2         5 0.5452
## 293 261   control  none  13      20                 0         0 0.0000
## 294 267   control  none  14      20                 0         0 0.0000
## 295 272   control  none  15      20                 0         0 0.0000
## 296 279   control  none  16      20                 0         0 0.0000
## 297 282   control  none  17      20                 0         0 0.0000
## 298 289   control  none  18      20                 0         0 0.0000
## 299 294   control  none  19      20                 0         0 0.0000
## 300 300   control  none  20      20                 2         7 0.7728
## 301 305     shade  high   1       0                 0         0 0.0000
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##     Ephedra.above Ephedra.below Ephedra.biomass brome.biomass          test
## 1         0.00550       0.00120         0.00670       0.00000  clipped-once
## 2         0.02650       0.00350         0.03000       0.09180  clipped-once
## 3         0.01360       0.00510         0.01870       0.25030  clipped-once
## 4         0.00000       0.00000         0.00000       0.00000  clipped-once
## 5         0.02130       0.00530         0.02660       0.12160  clipped-once
## 6         0.00000       0.00000         0.00000       0.29580  clipped-once
## 7         0.00000       0.00000         0.00000       0.26070  clipped-once
## 8         0.01650       0.00820         0.02470       0.18090  clipped-once
## 9         0.00000       0.00000         0.00000       0.20730  clipped-once
## 10        0.00000       0.00000         0.00000       0.28800  clipped-once
## 11        0.00000       0.00000         0.00000       0.00000  clipped-once
## 12        0.03620       0.00600         0.04220       0.37190  clipped-once
## 13        0.00000       0.00000         0.00000       0.05550  clipped-once
## 14        0.00000       0.00000         0.00000       0.00000  clipped-once
## 15        0.00000       0.00000         0.00000       0.19680  clipped-once
## 16        0.00000       0.00000         0.00000       0.00000  clipped-once
## 17        0.02370       0.00460         0.02830       0.09410  clipped-once
## 18        0.00000       0.00000         0.00000       0.64990  clipped-once
## 19        0.00000       0.00000         0.00000       0.37030  clipped-once
## 20        0.00000       0.00000         0.00000       0.38870  clipped-once
## 21        0.00000       0.00000         0.00000       0.10390 clipped-twice
## 22        0.00000       0.00000         0.00000       0.12920 clipped-twice
## 23        0.01850       0.00000         0.01850       0.08190 clipped-twice
## 24        0.01300       0.00080         0.01380       0.00000 clipped-twice
## 25        0.00000       0.00000         0.00000       0.20410 clipped-twice
## 26        0.00000       0.00000         0.00000       0.12900 clipped-twice
## 27        0.00000       0.00000         0.00000       0.11510 clipped-twice
## 28        0.01280       0.00530         0.01810       0.07580 clipped-twice
## 29        0.00000       0.00000         0.00000       0.10430 clipped-twice
## 30        0.02450       0.00260         0.02710       0.30570 clipped-twice
## 31        0.03030       0.00830         0.03860       0.00000 clipped-twice
## 32        0.04260       0.00930         0.05190       0.22820 clipped-twice
## 33        0.00000       0.00000         0.00000       0.16880 clipped-twice
## 34        0.00930       0.00320         0.01250       0.00000 clipped-twice
## 35        0.00000       0.00000         0.00000       0.63810 clipped-twice
## 36        0.01810       0.00310         0.02120       0.00000 clipped-twice
## 37        0.01650       0.00270         0.01920       0.05580 clipped-twice
## 38        0.01550       0.00080         0.01630       0.25570 clipped-twice
## 39        0.00000       0.00000         0.00000       0.31530 clipped-twice
## 40        0.00000       0.00000         0.00000       0.43460 clipped-twice
## 41        0.01070       0.00080         0.01150       0.28450  clipped-once
## 42        0.00000       0.00000         0.00000       0.18080  clipped-once
## 43        0.00000       0.00000         0.00000       0.00000  clipped-once
## 44        0.00000       0.00000         0.00000       0.51090  clipped-once
## 45        0.00000       0.00000         0.00000       0.49770  clipped-once
## 46        0.00000       0.00000         0.00000       0.37290  clipped-once
## 47        0.00000       0.00000         0.00000       0.00000  clipped-once
## 48        0.02490       0.00640         0.03130       0.48910  clipped-once
## 49        0.00000       0.00000         0.00000       0.26980  clipped-once
## 50        0.03850       0.00740         0.04590       0.09020  clipped-once
## 51        0.00000       0.00000         0.00000       0.06860  clipped-once
## 52        0.00000       0.00000         0.00000       0.00000  clipped-once
## 53        0.00000       0.00000         0.00000       0.04360  clipped-once
## 54        0.00000       0.00000         0.00000       0.04860  clipped-once
## 55        0.00000       0.00000         0.00000       0.34990  clipped-once
## 56        0.00000       0.00000         0.00000       0.08430  clipped-once
## 57        0.00000       0.00000         0.00000       0.05540  clipped-once
## 58        0.01160       0.00350         0.01510       0.42220  clipped-once
## 59        0.05680       0.00790         0.06470       0.08060  clipped-once
## 60        0.00000       0.00000         0.00000       0.14490  clipped-once
## 61        0.04010       0.01200         0.05210       0.22380 clipped-twice
## 62        0.02610       0.01290         0.03900       0.07840 clipped-twice
## 63        0.00000       0.00000         0.00000       0.00000 clipped-twice
## 64        0.01410       0.00560         0.01970       0.10500 clipped-twice
## 65        0.01290       0.00410         0.01700       0.31520 clipped-twice
## 66        0.03570       0.00750         0.04320       0.13820 clipped-twice
## 67        0.00000       0.00000         0.00000       0.00000 clipped-twice
## 68        0.00000       0.00000         0.00000       0.08840 clipped-twice
## 69        0.00000       0.00000         0.00000       0.20450 clipped-twice
## 70        0.00900       0.00360         0.01260       0.05780 clipped-twice
## 71        0.00000       0.00000         0.00000       0.07440 clipped-twice
## 72        0.00900       0.00250         0.01150       0.32930 clipped-twice
## 73        0.00000       0.00000         0.00000       0.03150 clipped-twice
## 74        0.00990       0.00500         0.01490       0.00000 clipped-twice
## 75        0.00000       0.00000         0.00000       0.29070 clipped-twice
## 76        0.00000       0.00000         0.00000       0.06400 clipped-twice
## 77        0.00000       0.00000         0.00000       0.36160 clipped-twice
## 78        0.00000       0.00000         0.00000       0.08940 clipped-twice
## 79        0.02130       0.00510         0.02640       0.06920 clipped-twice
## 80        0.00000       0.00000         0.00000       0.14790 clipped-twice
## 81        0.00000       0.00000         0.00000       0.97380  clipped-once
## 82        0.00000       0.00000         0.00000       0.07510  clipped-once
## 83        0.00000       0.00000         0.00000       0.00000  clipped-once
## 84        0.02700       0.00230         0.02930       0.37440  clipped-once
## 85        0.00000       0.00000         0.00000       0.00000  clipped-once
## 86        0.03300       0.00550         0.03850       0.05470  clipped-once
## 87        0.00000       0.00000         0.00000       0.28710  clipped-once
## 88        0.00000       0.00000         0.00000       0.13070  clipped-once
## 89        0.00000       0.00000         0.00000       0.00000  clipped-once
## 90        0.00000       0.00000         0.00000       0.00000  clipped-once
## 91        0.04280       0.00770         0.05050       0.14800  clipped-once
## 92        0.00000       0.00000         0.00000       0.00000  clipped-once
## 93        0.00000       0.00000         0.00000       0.06470  clipped-once
## 94        0.00000       0.00000         0.00000       0.36080  clipped-once
## 95        0.00000       0.00000         0.00000       0.00000  clipped-once
## 96        0.00560       0.00270         0.00830       0.48060  clipped-once
## 97        0.00000       0.00000         0.00000       0.18510  clipped-once
## 98        0.00000       0.00000         0.00000       0.03410  clipped-once
## 99        0.00850       0.00180         0.01030       0.24800  clipped-once
## 100       0.01120       0.00560         0.01680       0.12510  clipped-once
## 101       0.00000       0.00000         0.00000       0.22280 clipped-twice
## 102       0.00000       0.00000         0.00000       0.27740 clipped-twice
## 103       0.00000       0.00000         0.00000       0.00000 clipped-twice
## 104       0.00000       0.00000         0.00000       0.16200 clipped-twice
## 105       0.01540       0.00220         0.01760       0.00000 clipped-twice
## 106       0.00000       0.00000         0.00000       0.13150 clipped-twice
## 107       0.01820       0.00520         0.02340       0.13440 clipped-twice
## 108       0.04970       0.01330         0.06300       0.19300 clipped-twice
## 109       0.01480       0.00230         0.01710       0.00000 clipped-twice
## 110       0.01200       0.00220         0.01420       0.04960 clipped-twice
## 111       0.00000       0.00000         0.00000       0.15610 clipped-twice
## 112       0.00000       0.00000         0.00000       0.49510 clipped-twice
## 113       0.00820       0.00220         0.01040       0.07590 clipped-twice
## 114       0.00000       0.00000         0.00000       0.55020 clipped-twice
## 115       0.00000       0.00000         0.00000       0.00000 clipped-twice
## 116       0.00000       0.00000         0.00000       0.74260 clipped-twice
## 117       0.00000       0.00000         0.00000       0.23590 clipped-twice
## 118       0.00000       0.00000         0.00000       0.06120 clipped-twice
## 119       0.00150       0.00160         0.00310       0.09730 clipped-twice
## 120       0.00000       0.00000         0.00000       0.07230 clipped-twice
## 121       0.02430       0.00680         0.03110       0.34550  clipped-once
## 122       0.00000       0.00000         0.00000       0.08370  clipped-once
## 123       0.00000       0.00000         0.00000       0.52100  clipped-once
## 124       0.02340       0.00480         0.02820       0.17470  clipped-once
## 125       0.00000       0.00000         0.00000       0.00000  clipped-once
## 126       0.00000       0.00000         0.00000       0.36200  clipped-once
## 127       0.00000       0.00000         0.00000       0.00000  clipped-once
## 128       0.00000       0.00000         0.00000       0.11290  clipped-once
## 129       0.02560       0.00530         0.03090       0.11980  clipped-once
## 130       0.01280       0.00260         0.01540       0.29680  clipped-once
## 131       0.00000       0.00000         0.00000       0.03630  clipped-once
## 132       0.01900       0.00490         0.02390       0.12700  clipped-once
## 133       0.02270       0.00920         0.03190       0.03560  clipped-once
## 134       0.04150       0.00480         0.04630       0.31550  clipped-once
## 135       0.00000       0.00000         0.00000       0.00000  clipped-once
## 136       0.00000       0.00000         0.00000       0.00000  clipped-once
## 137       0.00000       0.00000         0.00000       0.10080  clipped-once
## 138       0.00000       0.00000         0.00000       0.00000  clipped-once
## 139       0.00000       0.00000         0.00000       0.75300  clipped-once
## 140       0.00000       0.00000         0.00000       0.11050  clipped-once
## 141       0.00000       0.00000         0.00000       0.11840 clipped-twice
## 142       0.02530       0.00610         0.03140       0.07840 clipped-twice
## 143       0.00000       0.00000         0.00000       0.04040 clipped-twice
## 144       0.00000       0.00000         0.00000       0.21310 clipped-twice
## 145       0.00820       0.00490         0.01310       0.00000 clipped-twice
## 146       0.00300       0.00060         0.00360       0.20720 clipped-twice
## 147       0.00000       0.00000         0.00000       0.11400 clipped-twice
## 148       0.00000       0.00000         0.00000       0.06970 clipped-twice
## 149       0.00000       0.00000         0.00000       0.08230 clipped-twice
## 150       0.00000       0.00000         0.00000       0.26620 clipped-twice
## 151       0.00000       0.00000         0.00000       0.05840 clipped-twice
## 152       0.00000       0.00000         0.00000       0.04610 clipped-twice
## 153       0.00000       0.00000         0.00000       0.09150 clipped-twice
## 154       0.00000       0.00000         0.00000       0.50060 clipped-twice
## 155       0.00000       0.00000         0.00000       0.00000 clipped-twice
## 156       0.00000       0.00000         0.00000       0.00000 clipped-twice
## 157       0.00000       0.00000         0.00000       0.11740 clipped-twice
## 158       0.01170       0.00270         0.01440       0.00000 clipped-twice
## 159       0.00000       0.00000         0.00000       0.40220 clipped-twice
## 160       0.01240       0.00200         0.01440       0.05850 clipped-twice
## 161       0.00000       0.00000         0.00000       0.75040  clipped-once
## 162       0.06560       0.01170         0.07730       0.00000  clipped-once
## 163       0.00000       0.00000         0.00000       0.00000  clipped-once
## 164       0.03600       0.00780         0.04380       0.13120  clipped-once
## 165       0.00000       0.00000         0.00000       0.33800  clipped-once
## 166       0.01150       0.00230         0.01380       0.12240  clipped-once
## 167       0.00000       0.00000         0.00000       0.22720  clipped-once
## 168       0.00000       0.00000         0.00000       0.18500  clipped-once
## 169       0.03550       0.00100         0.03650       0.14660  clipped-once
## 170       0.01950       0.00380         0.02330       0.29450  clipped-once
## 171       0.00810       0.00500         0.01310       0.40970  clipped-once
## 172       0.01220       0.00430         0.01650       0.00000  clipped-once
## 173       0.00000       0.00000         0.00000       0.35110  clipped-once
## 174       0.00000       0.00000         0.00000       0.59720  clipped-once
## 175       0.00000       0.00000         0.00000       0.00000  clipped-once
## 176       0.00000       0.00000         0.00000       0.00000  clipped-once
## 177       0.00000       0.00000         0.00000       0.20830  clipped-once
## 178       0.00000       0.00000         0.00000       0.00000  clipped-once
## 179       0.00000       0.00000         0.00000       0.00000  clipped-once
## 180       0.00000       0.00000         0.00000       0.14880  clipped-once
## 181       0.00770       0.00000         0.00770       0.16940 clipped-twice
## 182       0.01310       0.00270         0.01580       0.00000 clipped-twice
## 183       0.00000       0.00000         0.00000       0.00000 clipped-twice
## 184       0.00000       0.00000         0.00000       0.08240 clipped-twice
## 185       0.00000       0.00000         0.00000       0.22150 clipped-twice
## 186       0.00720       0.00080         0.00800       0.08980 clipped-twice
## 187       0.00000       0.00000         0.00000       0.05690 clipped-twice
## 188       0.00000       0.00000         0.00000       0.05500 clipped-twice
## 189       0.00000       0.00000         0.00000       0.63270 clipped-twice
## 190       0.00000       0.00000         0.00000       0.30780 clipped-twice
## 191       0.03100       0.00870         0.03970       0.23010 clipped-twice
## 192       0.01410       0.00130         0.01540       0.00000 clipped-twice
## 193       0.01750       0.00130         0.01880       0.46290 clipped-twice
## 194       0.01240       0.00260         0.01500       0.21450 clipped-twice
## 195       0.00000       0.00000         0.00000       0.00000 clipped-twice
## 196       0.00000       0.00000         0.00000       0.00000 clipped-twice
## 197       0.00000       0.00000         0.00000       0.52390 clipped-twice
## 198       0.00000       0.00000         0.00000       0.00000 clipped-twice
## 199       0.00000       0.00000         0.00000       0.05120 clipped-twice
## 200       0.01320       0.00140         0.01460       0.00000 clipped-twice
## 201       0.00000       0.00000         0.00000       0.26740  control-none
## 202       0.01110       0.00190         0.01300       0.15880  control-none
## 203       0.03880       0.00270         0.04150       0.10360  control-none
## 204       0.00000       0.00000         0.00000       0.00000  control-none
## 205       0.00000       0.00000         0.00000       0.00000  control-none
## 206       0.03070       0.00230         0.03300       0.12130  control-none
## 207       0.00000       0.00000         0.00000       0.19280  control-none
## 208       0.00000       0.00000         0.00000       0.17980  control-none
## 209       0.06990       0.01180         0.07180       0.79270  control-none
## 210       0.03840       0.00690         0.04530       0.58480  control-none
## 211       0.00000       0.00000         0.00000       0.00000  control-none
## 212       0.00000       0.00000         0.00000       0.54080  control-none
## 213       0.00000       0.00000         0.00000       0.28460  control-none
## 214       0.04600       0.00760         0.05360       0.00000  control-none
## 215       0.00000       0.00000         0.00000       0.64600  control-none
## 216       0.02830       0.00550         0.03380       0.00000  control-none
## 217       0.00000       0.00000         0.00000       0.18060  control-none
## 218       0.00000       0.00000         0.00000       0.51500  control-none
## 219       0.00000       0.00000         0.00000       0.47590  control-none
## 220       0.00000       0.00000         0.00000       0.62080  control-none
## 221       0.01240       0.00530         0.01770       0.33220  control-none
## 222       0.08860       0.01020         0.09880       0.24710  control-none
## 223       0.00000       0.00000         0.00000       0.23960  control-none
## 224       0.00350       0.00000         0.00350       0.47170  control-none
## 225       0.04330       0.00440         0.04770       0.26980  control-none
## 226       0.03900       0.00650         0.04550       0.44520  control-none
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## 700       0.02370       0.00400         0.02770       0.27220     water-low

recruit[is.na(recruit)] <- 0

recruit[,"eph.rate"] <- recruit$ephedra.emergence/3*100

## Percent of ephedra seedlings becoming established
mean(recruit$eph.rate)

## [1] 9.857143

## Percent of brome seedlings becoming established
mean(recruit$brome.prop.begin)

## [1] 51.36429

Shrub-plant facilitation results

## load plant comp data
plant <- read.csv("data//ephedra.plantcomp.csv")

library(lmerTest)

## 
## Attaching package: 'lmerTest'

## The following object is masked from 'package:lme4':
## 
##     lmer

## The following object is masked from 'package:stats':
## 
##     step

## community measures
plant[,"abd"] <- apply(plant[,9:48], 1, function(x) sum(x, na.rm=T)) ## abundance 
plant[,"rich"] <- apply(plant[,9:48], 1, function(x) sum(x>0, na.rm=T))

## percent brome
plant[is.na(plant)] <- 0
mean(plant[,"B.rubens"]/plant[,"abd"])*100

## [1] 69.22444

## fit a linear model
m1 <- glmer.nb(abd ~ microsite + (1|year) + (1|site), data=plant)
summary(m1)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Negative Binomial(9.0118)  ( log )
## Formula: abd ~ microsite + (1 | year) + (1 | site)
##    Data: plant
## 
##      AIC      BIC   logLik deviance df.resid 
##   4883.1   4903.7  -2436.6   4873.1      445 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.4761 -0.6159 -0.0603  0.5463  3.2187 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  year   (Intercept) 0.003222 0.05677 
##  site   (Intercept) 0.078784 0.28069 
## Number of obs: 450, groups:  year, 3; site, 3
## 
## Fixed effects:
##                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)     4.91598    0.16702  29.433   <2e-16 ***
## micrositeshrub  0.31954    0.03261   9.798   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## microstshrb -0.098

car::Anova(m1, test="Chisq")

## Registered S3 methods overwritten by 'car':
##   method                          from
##   influence.merMod                lme4
##   cooks.distance.influence.merMod lme4
##   dfbeta.influence.merMod         lme4
##   dfbetas.influence.merMod        lme4

## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: abd
##            Chisq Df Pr(>Chisq)    
## microsite 95.992  1  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

m2 <- glmer.nb(rich ~ microsite + (1|year) + (1|site), data=plant)

## Warning in theta.ml(Y, mu, weights = object@resp$weights, limit = limit, :
## iteration limit reached

summary(m2)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Negative Binomial(329887.7)  ( log )
## Formula: rich ~ microsite + (1 | year) + (1 | site)
##    Data: plant
## 
##      AIC      BIC   logLik deviance df.resid 
##   1399.3   1419.9   -694.7   1389.3      445 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.10029 -0.48707  0.01885  0.34541  1.89031 
## 
## Random effects:
##  Groups Name        Variance  Std.Dev.
##  year   (Intercept) 0.0008052 0.02838 
##  site   (Intercept) 0.0374271 0.19346 
## Number of obs: 450, groups:  year, 3; site, 3
## 
## Fixed effects:
##                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)     1.19133    0.11531  10.331   <2e-16 ***
## micrositeshrub -0.57803    0.05999  -9.636   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## microstshrb -0.177

car::Anova(m2, test="Chisq")

## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: rich
##            Chisq Df Pr(>Chisq)    
## microsite 92.855  1  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

### calculate averages and variance
plantavg <- plant %>% group_by(microsite) %>% summarize(ABD=mean(abd), RICH=mean(rich),ABD.se=se(abd)*1.96,  RICH.se=se(rich)*1.96 )

##abundance
abd <- plantavg[,c(1:2,4)]
abd[,2:3] <- abd[,2:3]/0.25

## plot
plot1 <- ggplot(abd, aes(x=microsite, y=ABD, fill=microsite)) + geom_bar(stat="identity", position=position_dodge(width=0.9), color="black") + ylab(expression("plant density (m"^2*")")) + theme_Publication() + geom_errorbar(aes(x=microsite, ymin=ABD-ABD.se, ymax=ABD+ABD.se), position=position_dodge(width=0.9), width=0) + xlab("") + scale_fill_brewer()

## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing

## richness
rich <- plantavg[,c(1,3,5)]


## plot
plot2 <- ggplot(rich, aes(x=microsite, y=RICH, fill=microsite)) + geom_bar(stat="identity", position=position_dodge(width=0.9), color="black") + ylab("species richness") + theme_Publication() + geom_errorbar(aes(x=microsite, ymin=RICH-RICH.se, ymax=RICH+RICH.se), position=position_dodge(width=0.9), width=0) + xlab("") + scale_fill_brewer()

## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing

require(gridExtra)

## Loading required package: gridExtra

## 
## Attaching package: 'gridExtra'

## The following object is masked from 'package:dplyr':
## 
##     combine

grid.arrange(plot1, plot2, nrow=2)

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## font family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

### compare just brome
plant[,"perBrome"] <- plant[,"B.rubens"]/plant[,"abd"]*100

m1 <- glmer(B.rubens/abd ~ microsite + (1|site) + (1|year), data=plant, family="binomial")

## Warning in eval(family$initialize, rho): non-integer #successes in a binomial
## glm!

summary(m1)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: B.rubens/abd ~ microsite + (1 | site) + (1 | year)
##    Data: plant
## 
##      AIC      BIC   logLik deviance df.resid 
##    305.3    321.8   -148.7    297.3      446 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.3433 -0.1943  0.0857  0.2643  1.2188 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  site   (Intercept) 2.6488   1.6275  
##  year   (Intercept) 0.6417   0.8011  
## Number of obs: 450, groups:  site, 3; year, 3
## 
## Fixed effects:
##                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)     -0.2411     1.0640  -0.227    0.821    
## micrositeshrub   4.2433     0.4690   9.048   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## microstshrb -0.099

car::Anova(m1, test="Chisq")

## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: B.rubens/abd
##            Chisq Df Pr(>Chisq)    
## microsite 81.858  1  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

m2 <- glmer.nb(B.rubens ~ microsite + (1|site) + (1|year), data=plant)
summary(m2)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Negative Binomial(3.1316)  ( log )
## Formula: B.rubens ~ microsite + (1 | site) + (1 | year)
##    Data: plant
## 
##      AIC      BIC   logLik deviance df.resid 
##   4921.8   4942.3  -2455.9   4911.8      445 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6697 -0.6630 -0.1346  0.5268  2.8941 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  site   (Intercept) 0.26562  0.5154  
##  year   (Intercept) 0.03112  0.1764  
## Number of obs: 450, groups:  site, 3; year, 3
## 
## Fixed effects:
##                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)     4.13618    0.31718   13.04   <2e-16 ***
## micrositeshrub  0.99767    0.05745   17.37   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## microstshrb -0.093

car::Anova(m2, test="Chisq")

## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: B.rubens
##            Chisq Df Pr(>Chisq)    
## microsite 301.57  1  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

plant %>% group_by(microsite) %>% summarize(avg=mean(B.rubens), error=se(B.rubens))

## # A tibble: 2 x 3
##   microsite   avg error
##   <fct>     <dbl> <dbl>
## 1 open       82.4  4.02
## 2 shrub     174.   4.95